Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets

2020/11/19 by Marco Castelli, Francesco Catino, Castelli, Marco +3 · 1 citation
Mathematics · #16T25 #20E22 #20N02 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16T25 #msc:20E22 #msc:20N02 #msc:81R50

paper · pdf · doi:10.48550/arxiv.2011.10083

arxiv created 2020/11/19 · arxiv updated 2020/11/23

Abstract

Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Yang-Baxter equation having specific imprimitivity blocks. Moreover, we study one-generator left braces of multipermutation level 2.

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• A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation

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